# Adaptive Modeling of Uncertainties for Traffic Forecasting

arXiv: https://arxiv.org/abs/2303.09273 · HTML: https://mlsanity.com/paper/2303.09273/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 61 references that are in the map.
- First posted on arXiv 16 Mar 2023.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks](https://mlsanity.com/paper/1905.11001/) (2019)
- [A Probabilistic U-Net for Segmentation of Ambiguous Images](https://mlsanity.com/paper/1806.05034/) (2018)
- [Time Series Data Augmentation for Deep Learning: A Survey](https://mlsanity.com/paper/2002.12478/) (2020)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantification](https://mlsanity.com/paper/2011.09588/) (2020)
- [DL-Traff: Survey and Benchmark of Deep Learning Models for Urban Traffic Prediction](https://mlsanity.com/paper/2108.09091/) (2021)
- [Locally Valid and Discriminative Prediction Intervals for Deep Learning Models](https://mlsanity.com/paper/2106.00225/) (2021)
- [Dual-Consistency Semi-Supervised Learning with Uncertainty Quantification for COVID-19 Lesion Segmentation from CT Images](https://mlsanity.com/paper/2104.03225/) (2021)
- [Uncertainty Quantification for Traffic Forecasting: A Unified Approach](https://mlsanity.com/paper/2208.05875/) (2022)
- [STUaNet: Understanding uncertainty in spatiotemporal collective human mobility](https://mlsanity.com/paper/2102.06027/) (2021)
- [From Data to Actions in Intelligent Transportation Systems: a Prescription of Functional Requirements for Model Actionability](https://mlsanity.com/paper/2002.02210/) (2020)
- [Decentralized Ride-Sharing and Vehicle-Pooling Based on Fair Cost-Sharing Mechanisms](https://mlsanity.com/paper/2007.08064/) (2020)

## Built on by (most cited first, 6 of 6)

- [SAUC: Sparsity-Aware Uncertainty Calibration for Spatiotemporal Prediction with Graph Neural Networks](https://mlsanity.com/paper/2409.08766/) (2024)
- [Do Time Series Foundation Model Benchmarks Hide Regime-Dependent Failures? Evidence from Traffic Speed Forecasting](https://mlsanity.com/paper/2606.18367/) (2026)
- [Unveiling Stochasticity: Universal Multi-modal Probabilistic Modeling for Traffic Forecasting](https://mlsanity.com/paper/2604.16084/) (2026)
- [Causally-Aware Spatio-Temporal Multi-Graph Convolution Network for Accurate and Reliable Traffic Prediction](https://mlsanity.com/paper/2408.13293/) (2024)
- [CONTINA: Confidence Interval for Traffic Demand Prediction with Coverage Guarantee](https://mlsanity.com/paper/2504.13961/) (2025)
- [Joint upper-bound coverage and route-choice utility: an empirical evaluation on two urban proxy tasks](https://mlsanity.com/paper/2610.06995/) (2026)

## Abstract (arXiv)

Deep neural networks (DNNs) have emerged as a dominant approach for developing traffic forecasting models. These models are typically trained to minimize error on averaged test cases and produce a single-point prediction, such as a scalar value for traffic speed or travel time. However, single-point predictions fail to account for prediction uncertainty that is critical for many transportation management scenarios, such as determining the best- or worst-case arrival time. We present QuanTraffic, a generic framework to enhance the capability of an arbitrary DNN model for uncertainty modeling. QuanTraffic requires little human involvement and does not change the base DNN architecture during deployment. Instead, it automatically learns a standard quantile function during the DNN model training to produce a prediction interval for the single-point prediction. The prediction interval defines a range where the true value of the traffic prediction is likely to fall. Furthermore, QuanTraffic develops an adaptive scheme that dynamically adjusts the prediction interval based on the location and prediction window of the test input. We evaluated QuanTraffic by applying it to five representative DNN models for traffic forecasting across seven public datasets. We then compared QuanTraffic against five uncertainty quantification methods. Compared to the baseline uncertainty modeling techniques, QuanTraffic with base DNN architectures delivers consistently better and more robust performance than the existing ones on the reported datasets.